The term "pagan" is typically used in modern times to refer to anyone who believes in a polytheistic religion. Therefore, we would say that the Greeks and Romans were pagans because they believed in many gods. We would also say that the ancient Celts were pagans because they believed in gods and spirits and such. So the term really covers a wide variety of beliefs, from religions like those of the Celts and of ancient Shinto Japan to much more formalized religions like those of the Romans.
These beliefs differ from Catholicism most clearly in the fact that they are polytheistic. Catholics, like all Christians, believe in one God only. In the context of medieval Europe (since you tagged this with "medieval") a pagan might also believe, for example, in spirits that brought good or bad luck to harvests or child-bearing or animal rearing. None of these would have been officially acceptable to the Catholic Church.
Another part of the answer that might be relevant is the fact that Catholicism is based on a patriarchal society, with an emphasis on the males. Many of the pagan societies were based on a matriarchal society, with the Earth being considered the Mother and giver of life. With this fundamental difference, the attitude of the religion is perceived verry differently. In historic times, women cared for the children throuh the infancy and young childhood, teaching them about house and home annd keeping them in their "apron strings."When boys were old enough, they joined the men and left the women behind.
The pagan religions believed women were the bearers of religion and cherished their understanding. Catholic religion, as well as all of the other monotheistic religions, believe men are the bearers of the religion. It is the difference between believing the heart of the religion is nuturing and caretaking versus religion as rules for living, hunting, and ruling as well as what needed to happen to be good soldiers -for your king or for God. This basic belief changed the way that people interacted. Instead of caretaking being the focus of religion, following the tenents was vital. The pagans had individually created rituals and and beliefs whereas the catholic faith was written down and strictly passed from one person to the next. Beingg a pagan meant a wide range of things you might or might not believe, but if you were Catholic, there was a specific set of beliefs to which you ascribed.
There are many other differences, but this is a basic difference that changed the world.